Isn't it, in the end, just a notational issue? Quaternions are unit bivectors. Up to a slightly annoying sign change, quaternions which are noted as i, j and

Isn't it, in the end, just a notational issue? Quaternions are unit bivectors. Up to a slightly annoying sign change, quaternions which are noted as i, j and k correspond to bivectors jk, ki and ij, don't they? There should be a way to write a library that translates geometric algebra notations into their corresponding quaternion ones, and reciprocally.